Consider the following machine repair problem. A facility contains four identical machines that op erate independently. Once a machine starts operating, the time until it fails is an exponential random variable having rate 1 = 0.1 failure per hour. The time required for a technician to restore a failed ma- chine to its original status is an exponential random variable having rate p = 0.4 repair per hour. Three equally trained technicians are assigned the duty of repairing failed machines. Determine the following 1. the long-run average number of busy technicians. 2. the long-run average number of machines operating 3. the long-run average number of machines waiting for repair. The manager of the facility can employ only upto 4 technicians. Every hour of machine downtime costs the facility $275. Each technicians are paid $x per hour. Find x such that employing 3 technicians is the best choice. (Hint: Compute the long-run average cost per hour for each of 4, 3, 2 and 1 technicians as a function of x, and find the x for range of x) where employing 3 technicians incurs the least cost :) Consider the following machine repair problem. A facility contains four identical machines that op erate independently. Once a machine starts operating, the time until it fails is an exponential random variable having rate 1 = 0.1 failure per hour. The time required for a technician to restore a failed ma- chine to its original status is an exponential random variable having rate p = 0.4 repair per hour. Three equally trained technicians are assigned the duty of repairing failed machines. Determine the following 1. the long-run average number of busy technicians. 2. the long-run average number of machines operating 3. the long-run average number of machines waiting for repair. The manager of the facility can employ only upto 4 technicians. Every hour of machine downtime costs the facility $275. Each technicians are paid $x per hour. Find x such that employing 3 technicians is the best choice. (Hint: Compute the long-run average cost per hour for each of 4, 3, 2 and 1 technicians as a function of x, and find the x for range of x) where employing 3 technicians incurs the least cost :)